A new report says that it would take a further 20 years for a third of boardroom jobs to be held by women. Photograph: moodboard/Alamy

The "shocking" lack of women on the boards of the UK's biggest companies was highlighted on Thursday by analysis claiming that at the current pace of recruitment it would take 20 years for one in three of directors in the boardroom to be female.

A report by Deloitte found that 20% of companies in the FTSE 100 had no women in their boardrooms and just 5% of executive positions were held by women.

Carol Arrowsmith, partner in Deloitte's remuneration team, said: "The number of companies where there are no female board members is quite shocking. It is of particular concern that the proportion of women on boards has only increased from 5% to 9% in 10 years. At this rate, it would take another 20 years to reach the position of 30% female board representation, which is the aim of the 30% Club."

The aspirations of the 30% Club, set up by chairmen keen to bolster female representation on company boards, are similar to those set out by Lord Davies, who in his review of boardrooms in February called for UK companies to have 25% female board membership by 2015.

Davies had recommended in February that UK companies take six months to publish their own targets for bolstering female presence on their boards but an official update published on Wednesday found that only 33 companies in the FTSE 100 had set such targets.

The research by Cranfield University published on Wednesday found that only 22.5% of all new boardroom appointments have been women. Only 14.2% of boardroom seats in the FTSE 100 are held by women – up from 12.5% in 2010 and in total, 21 women have been appointed to FTSE 100 boards since February. Only three of them are in executive positions – Lucinda Bell, who was named finance director of British Land, Laura Wade-Gery at Marks & Spencer and Tracy Robbins at Intercontinental Hotels. The rest, including Burberry finance director Stacey Cartwright, are to non-executive posts.

Davies, the former chairman of Standard Chartered, said more were needed. "This is about good business practice; it is also about securing performance. You need engagement and diversity in teams to achieve success. Too many UK boards and executive teams do not have it. We are working to change that," Davies said.

Ministers Vince Cable and Theresa May indicated they did not intend to make quotas mandatory. The business secretary and women's minister said: "There is still a long way to go and too many companies fail to recognise the potential of women in leadership positions. We remain optimistic, however, that the voluntary approach advocated by Lord Davies will deliver the necessary changes."

A reception was held in Downing Street on Wednesday evening and David Cameron is writing to firms urging them to sign up to targets.

Lawyers warned that legislation might be on the agenda if there was not enough action. "The current political support these issues have, both at home and in Europe, mean that if FTSE companies fail to make further significant progress with gender diversity issues voluntarily and in the short term, then the spectre of legislation and the introduction of quotas, as has happened elsewhere in Europe, may be seen as an inevitable consequence," said Mark Spinner, partner at international law firm Eversheds.

Professor Susan Vinnicombe, co-author of the Cranfield report, thought progress was being made. She said: "Our review reveals that the number of women in board positions is beginning to creep up, albeit quite slowly."

However, she also cited the type of appointments – 14 out of the 21 FTSE 100 new appointees and 20 of the 28 FTSE 250 new appointees had no prior experience in a boardroom of that size. "This suggests the appointment process is beginning to open up to new women. This is very positive and indicates that some chairmen and search consultancies are following Lord Davies's recommendations to broaden the talent pool."

Of the 33 firms which have set targets, only 10 expect to increase female representation to more than 10%. The Cranfield report said Rolls-Royce and bailed-out Lloyds Banking Group "stand out" for aiming to increase their female board membership by 20 to 23%.